At what temperature will oxygen molecules have the same root mean square speed as hydrogen Molecules at $200 K$ ?

527⁰C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1327⁰C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2127⁰C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2927⁰C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
2927⁰C

For oxygen:

$v_{r m s} = \sqrt{\frac{3 k T_{0}}{m_{0}}}$

For hydrogen:

$v_{r m s} = \sqrt{\frac{3 k T_{h}}{m_{h}}}$

The value of $v_{r m s}$ will be the same if

$\frac{T_{0}}{m_{0}} = \frac{T_{h}}{m_{h}}$

Or $T_{0} = \frac{m_{0}}{m_{h}} \times T_{h} = 16 \times 200$

$= 3200 K = 2927^{\circ} C$

Hence the correct choice is (d)

Suggest Corrections

Similar questions

At what temperature will the oxygen molecules have the same root mean square speed as hydrogen molecules at 200 K

35^{o} C

27^{\circ} C

{S O}_{2}

27^{o} C

Join BYJU'S Learning Program